A Modern Point of View on Anomalies

Monnier, Samuel

doi:10.1002/prop.201910012

Cited by 24 publications

(27 citation statements)

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“…Other important cases for which one can proceed analogously, and construct appropriate anomaly theories, are theories with self-dual fields in d = 4k + 2 dimensions, theories with Rarita-Schwinger fields, and theories where the Green-Schwarz anomaly cancellation mechanism operates. We refer the reader to [24,25] for a systematic discussion of such generalizations, and further references to the literature.…”

Section: (214)mentioning

confidence: 99%

“…The bosons could have any even charge and the symmetry would remain non-anomalous, but a natural choice is to take all bosons 24 We should note that in [89], this very same condition is obtained from requiring that the theory makes sense in a manifold with a generalized spin structure. 25 As discussed in section 3.4, once we assume U (1)B−L we can put the standard model in a Spin c manifold.…”

Section: Topological Superconductors and The Mssmmentioning

confidence: 99%

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Dai-Freed anomalies in particle physics

García-Etxebarria

Montero

2019

J. High Energ. Phys.

156

280

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Anomalies can be elegantly analyzed by means of the Dai-Freed theorem. In this framework it is natural to consider a refinement of traditional anomaly cancellation conditions, which sometimes leads to nontrivial extra constraints in the fermion spectrum. We analyze these more refined anomaly cancellation conditions in a variety of theories of physical interest, including the Standard Model and the SU (5) and Spin(10) GUTs, which we find to be anomaly free. Turning to discrete symmetries, we find that baryon triality has a Z 9 anomaly that only cancels if the number of generations is a multiple of 3. Assuming the existence of certain anomaly-free Z 4 symmetry we relate the fact that there are 16 fermions per generation of the Standard model -including right-handed neutrinos -to anomalies under time-reversal of boundary states in four-dimensional topological superconductors. A similar relation exists for the MSSM, only this time involving the number of gauginos and Higgsinos, and it is non-trivially, and remarkably, satisfied for the SU (3) × SU (2) × U (1) gauge group with two Higgs doublets. We relate the constraints we find to the well-known Ibañez-Ross ones, and discuss the dependence on UV data of the construction. Finally, we comment on the (non-)existence of K-theoretic θ angles in four dimensions. A On reduced bordism groups 63 B Tables of bordism groups of a point 64 C Bordism groups for Z k 65 D 3d currents 71 E Alternate generators for Ω Spin 5 (BZ n ) 73 -1 -An important technical point is that (2.4) and (2.5) require regularization as usual in quantum field theory. If a regularization preserving the symmetry G for an arbitrary background gauge field can be found, then (2.4) is not anomalous. In particular, this always happens whenever there is a G-invariant mass term m d d xψψ (2.8) for the fermions. In this case, Pauli-Villars regularization is available [5], which is manifestly gauge invariant.

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Section: (214)mentioning

confidence: 99%

Section: Topological Superconductors and The Mssmmentioning

confidence: 99%

Dai-Freed anomalies in particle physics

García-Etxebarria

Montero

2019

J. High Energ. Phys.

156

280

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“…For the purposes of studying the Heisenberg group of fluxes it is enough to consider the topological class K 1 (N 9 ) of the RR fields at the boundary [8]. 6 In analogy with the situation on QFT described above, we will assume that there is a Hilbert space H(N 9 ) associated to quantum boundary conditions, and that a specific choice of boundary conditions furnishes a vector in this Hilbert space. 7 (This prescription has been used before, for instance in the case of AdS/CFT boundary conditions [16].)…”

Section: Flux Operators and The Hilbert Space Hmentioning

confidence: 99%

“…We consider the (2, 0) theory of type g Γ compactified on M 6 = K3 × Σ, where Σ is a Riemann surface and the K3 is elliptically fibered. More concretely, we construct K3 as a hypersurface {P = 0} of degree (12,6) in a toric space Y described by the gauged linear sigma model with charges u 1 u 2 x y z C * 1 1 1 4 6 0 C * 0 0 2 3 1…”

Section: On the Global Structure Of N = 4 Theories With Duality Defectsmentioning

confidence: 99%

IIB flux non-commutativity and the global structure of field theories

García-Etxebarria

Heidenreich

Regalado

2019

J. High Energ. Phys.

181

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We discuss the origin of the choice of global structure for six dimensional (2, 0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of N = 4 theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of N = 4 ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional (1, 0) theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects. arXiv:1908.08027v2 [hep-th] 9 Oct 20191 The separation into background and intrinsic data is sometimes arbitrary: if we restrict ourselves to fourdimensional Yang-Mills theories with constant coupling τ we could view τ as part of the data defining T . However, if we wish to allow for the possibility that τ varies across M then we must include it as part of the background data to be specified for each manifold. The second interpretation will be more natural from the point of view in this paper, and such configurations will play an interesting role below.2 In this paper we will take M6 to be closed, Spin and orientable, and furthermore we will assume that the cohomology groups of M6 are freely generated, so there is no torsion. 3 The free, or "abelian", (2, 0) theory can be obtained by replacing C 2 /Γ by a single-centered Taub-NUT space.5 The two groups are related by the short exact sequence 0 → W 4 → H 4 (M6 × S 3 /Zn; U (1)) → Tor(H 5 (M6 × S 3 /ZN ; Z)) → 0 , with W 4 the group of topologically trivial C4 Wilson lines on M6 × S 3 /Zn.

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“… See Healey (2007) andRedhead (2003) for more detailed articulations of this general idea as well as some discussion about how issues of symmetry and quantization are related to more obviously philosophical issues.2 What follows are two simple examples of anomalies. SeeMonnier (2019) for more thorough but still relatively informal discussions of anomalous quantum field theories.…”

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confidence: 99%

The Substantial Role of Weyl Symmetry in Deriving General Relativity from String Theory

Dougherty¹

2021

Philos. of Sci.

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String theory reduces to general relativity in appropriate regimes. Huggett and Vistarini have given an account of this reduction that includes a deflationary thesis about symmetry: though the usual derivation of general relativity from string theory appeals to a premise about the theory's symmetry, Huggett and Vistarini argue that this premise plays no logical role. In this paper I disagree with their deflationary thesis and argue that their analysis is based on a popular but flawed conception of the interaction between symmetry and quantization. On this conception, quantization can break symmetries of the classical theory, and we must decide whether these symmetries should be reimposed. I argue that a better conception recognizes a tripartite distinction between ordinary, broken, and anomalous symmetries.

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A Modern Point of View on Anomalies

Cited by 24 publications

References 74 publications

Dai-Freed anomalies in particle physics

Dai-Freed anomalies in particle physics

IIB flux non-commutativity and the global structure of field theories

The Substantial Role of Weyl Symmetry in Deriving General Relativity from String Theory

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